Hybrid powertrains for vehicles utilize different power sources under different vehicle operating conditions. A hybrid powertrain with an electrically-variable transmission that can provide an input-split operating mode and a compound-split operating mode typically has two or three planetary gear sets and one or more motor/generators. The different operating modes are established by engaging brakes and/or clutches in different combinations and controlling the engine and motor/generators. The various power-split operating modes are advantageous, as they may be used to improve fuel economy by allowing the engine to operate at its most fuel efficient speed. A hybrid powertrain may also operate in an electric-only operating mode, in which only one or more motor/generators provide power to the transmission.